It sounds like that last bit says it all -

[IF YOU GET A GOOD ANALOG SIGNAL, THEN YOU'LL GET A GOOD PICTURE WITH THE CONVERTER BOX.

HOWEVER, IF YOU DON'T GET A GOOD ANALOG SIGNAL, AND YOU HAVE NO PICTURE (WHICH ESSENTIALLY IS WHAT IS HAPPENING AT THE MOMENT), IT SAYS "YOU WON'T GET ANY PICTURE".]

I suppose it you wanted to try the converter box - you could buy it and ask about being able to return it if you don't get a picture.

As I understand it the box just makes it so the new digital signal is can be picked up by the antenna and sent into the TV.
The digital signal must "travel" in the air in a similar way as the old analog signal. That must be why they say if no decent picture before digital, the box won't help get a better picture.

Yes they are broadcasting now - My aunt showed me her new TV {built in digital tuner} we saw all 4 OPB channels - before with antenna - got 1